1. Take a course in Critical Thinking. Or Introductory Informal Logic.
2. Be familiar with all the logical fallacies and cognitive biases. Start being aware of your thinking style. Be aware of your own errors in reasoning.
3. Engage in rigorous debates about issues you have strong views on. Watch more debates.
4. Practice switch-side debating, where you voluntarily try to build a case and defend a position you completely disagree with. It helps you to put yourself in your opponents shoes.
5. Write, and be critiqued. The ability to articulate your thoughts is just as important.